THE EFFECTS OF CRACK DEPTH ON THE J-INTEGRAL AND CTOD FRACTURE TOUGHNESS FOR WELDED BEND SPECIMENS

This work deals with the influence of crack depth on the fracture toughness at initiation of crack growth and the constraint factor in relationship between the J-integral and the crack tip opening displacement (CTOD). A series of tests were performed on high strength low alloyed HT80 steel welds, and the critical J-integral and CTOD were determined using the load versus load point displacement record from three-point bend specimens with 0.05 < a/W < 0.5. It was found that the fracture toughness for shallow cracks at the onset of crack growth was larger than that for deep cracks for the steel welds tested, but it is felt that there is no fixed relationship between these values in the welds tested. The constraint factor is also a function of crack depth, and values of the factor increase from 0.5 to 1.5 when a/W increases from about 0.05 to 0.5. The factors are not very sensitive to the crack tip materials (HAZ or weld metal) in the welds tested.     

Mechanical heterogeneity and validity of J-dominance in welded joints

Fracture criterion of the J-integral finds wide application in the integrity evaluation of welded components, but there exist some confused problems such as the dependence of the fracture toughness on the strength mis-matching and specimen geometry which need to be clarified. It is rough and unsuitable to attribute the variation of J-integral fracture parameter simply to the effect of mechanical heterogeneity. In the present paper, a two-dimensional finite element method is employed to analyze the distribution and variation of crack tip field of welded joints with different strength mis-matching in four kinds of specimen geometry, and then the validity of J-dominance in welded joints is investigated. It is found that the crack tip field of mis-matched joint is different from that of either the weld metal or base metal of which the joint is composed, but it is situated between those of weld metal and base metal. Under the plane strain, there is obvious difference in stress triaxiality for different strength mis-matched joints. The validity of J-dominance in welded joint can not be obtained by comparing whether the stress triaxiality meets that required by the HRR solution because of the existence of mechanical inhomogeneity. By ascertaining if the stress triaxiality of welded joint near the crack tip is dependent of specimen geometry, the conclusion can be arrived at: for plane stress the validity of J-dominance is valid, whilst for plane strain the validity of J-dominance is lost. Based on the above, attempt has been made to point out that the influence of mechanical heterogeneity on the fracture toughness of weldment arises from the variation of constraint intensity-crack tip stress triaxiality. Compared with the effect of mechanical heterogeneity on the stress triaxiality, the losing of validity of J-dominance in mis-matched joint under plane strain may play a more critical role in the variation of J-integral fracture parameter of weldment.     

Numerical simulation of time-dependent fracture of graded bimaterial metallic interfaces

Stationary cracks along and near interfaces between two time-dependent materials are simulated using the finite element method (FEM) to examine crack tip fields and candidate driving force parameters for crack growth. Plane strain conditions are assumed. In some cases, a thin transition layer is included between the two materials. This transition layer features a functionally graded blend of properties of the two materials. An example of such a system is that of weld metal (WM) and base metal (BM) in a weldment, with the transition layer corresponding to the heat-affected zone (HAZ). Numerical solutions for the stress and strain fields of homogeneous and heterogeneous Compact Tension (C(T)-type) specimens are presented. The equivalent domain integral technique is employed to compute the J-integral for elastic-plastic cases as well as the C(t)-integral and transition times for creep behavior. Results from parametric studies are curve-fit in terms of transition layer thickness and crack position, inelastic property mismatches, and other independent model parameters. Results indicate that the incorporation of functionally graded transition layer regions leads to less concentrated stress and strain components along interfaces ahead of the crack tip. It is also shown that the computed fracture parameters are influenced by the transition layer properties.     

Calculation of the energy J-integral for bodies with notches and cracks

The approximate solutions for calculation of the energy J-integral of a body both with a notch and with a crack under elastic-plastic loading have been obtained. The crack is considered as the limit case of a sharp notch. The method is based on stress concentration analysis near a notch/crack tip and the modified Neuber's approach. The HRR-model and the method based on an equation of equilibrium were also employed to calculate the J-integral. The influence of the strain hardening exponent on the J-integral is discussed. New aspects of the two-parameter J ^* _c-fracture criterion for a body with a short crack are studied. A theoretical investigation of the effect of the applied critical stress (or the crack length) on the strain fields ahead of the crack tip has been carried out.     

Crack growth resistance behavior of a functionally graded material: computational studies

This paper describes crack growth resistance simulation in a ceramic/metal functionally graded material (FGM) using a cohesive zone ahead of the crack front. The plasticity in the background (bulk) material follows J₂ flow theory with the flow properties determined by a volume fraction based, elastic-plastic model (extension of the original Tamura-Tomota-Ozawa model). A phenomenological, cohesive zone model with six material-dependent parameters (the cohesive energy densities and the peak cohesive tractions of the ceramic and metal phases, respectively, and two cohesive gradation parameters) describes the constitutive response of the cohesive zone. Crack growth occurs when the complete separation of the cohesive surfaces takes place. The crack growth resistance of the FGM is characterized by a rising J-integral with crack extension (averaged over the specimen thickness) computed using a domain integral (DI) formulation. The 3-D analyses are performed using WARP3D, a fracture mechanics research finite element code, which incorporates solid elements with graded elastic and plastic properties and interface-cohesive elements coupled with the functionally graded cohesive zone model. The paper describes applications of the cohesive zone model and the DI method to compute the J resistance curves for both single-edge notch bend, SE(B), and single-edge notch tension, SE(T), specimens having properties of a TiB/Ti FGM. The numerical results show that the TiB/Ti FGM exhibits significant crack growth resistance behavior when the crack grows from the ceramic-rich region into the metal-rich region. Under these conditions, the J-integral is generally higher than the cohesive energy density at the crack tip even when the background material response remains linearly elastic, which contrasts with the case for homogeneous materials wherein the J-integral equals the cohesive energy density for a quasi-statically growing crack.     

A numerical and experimental investigation on the use of J-integral

Finite element analysis was used to determine numerically Rice's J-integral values in centrally notched plates of 4340 steel. These numerical values were compared with corresponding J-integral values using Dugdale model and antiplane strain model with a power law hardening of n = 0.3. J-integral was also computed for a crack extending into its own plastic yield region under constant loading. For increasing level of loading, σ, the rate of increase in J-integral decreases and J-integral remains almost constant at $\text{σ}\text{σ}{}_{\mathrm{YS}}\text{= 1}$ under such crack extension.A limited number of fracture tests were conducted with centrally notched 4340 steel specimens heat treated to yield strength levels of 150,180, 210 and 240 ksi. Fracture data showed that the critical J-integral, calculated and measured, is insensitive to crack tip sharpness for the lower strength 4340 material and thus the J_c fracture criteria appears suited in correlating fracture data.     

Fluctuation of J-integral due to grain arrangement of Ni-based directionally solidified superalloy

The effect of local anisotropy due to the arrangement of anisotropic and arbitrary shaped grains of a directionally solidified superalloy on the J-integral is investigated by means of finite element analyses, where the models simulate the grain shape, its orientation, and the crack path of real material. The magnitudes of J_aniso, obtained by a detailed model, where most of grains are simulated, shows a stepwise change against the crack length a. This is mainly caused by the anisotropy of the grain at the crack tip. J_CV, obtained by a simplified model, where only the grains in the vicinity of the crack path are simulated, shows the same stepwise change as J_aniso. It elucidates that the anisotropy in the vicinity of the crack path is the dominant factor for the fluctuation of J_aniso. The magnitude of J_aniso and J_CV, however, are different from each other in detail. A large inhomogeneous area such as a cluster of grains and a large grain has a far-field influence and is mainly responsible for the differences between J_aniso and J_CV.     

On J-integral and potential energy variation

The divergence theorem has been used in a region containing the crack tip to derive the J-integral from the potential energy variation in most fracture mechanics books. Such a derivation is flawed because of the crack tip stress singularity. The present study describes a rigorous and straightforward derivation of the J-integral from the potential energy variation with crack extension by carefully addressing the effect of the crack tip singularity.     

Relations between structural intensity and J-integral

The present study introduces the concept of structural intensity, which can be interpreted as power flux, into fracture mechanics. It is derived theoretically that the normal component of the structural intensity along crack edge equals J-integral. SI is the power flux or vector representation of the J-integral at the crack tip. Using the finite element method, the structural intensity can be easily calculated. The numerically calculated structural intensity is adopted to visualize the J-integral of a crack tip. Directional power flow path and magnitude at the crack tip is demonstrated schematically with the structural intensity, which facilitates convenient evaluation of the crack propagation status.     

Micromechanical analysis of mechanical heterogeneity effect on the ductile tearing of weldments

The objective of this study is determination of the effect of mechanical heterogeneity on ductile crack initiation and propagation in weldments using micromechanical approach. Welded single-edge notched bend (SENB) specimens were experimentally and numerically analysed. Material properties of welded joint zones were estimated using a combined experimental and numerical procedure; strains on a smooth tensile specimen were determined using ARAMIS stereometric measuring system in order to obtain true stress – true strain curves. High-strength low-alloyed steel was used as base metal, in quenched and tempered condition. J–R curves and crack growth initiation values of fracture mechanics parameter were experimentally and numerically obtained for specimens with a pre-crack in the heat-affected zone (HAZ) and weld metal (WM). The complete Gurson model (CGM) was used in prediction of J–R curves and crack growth initiation. It is shown that the resistance to crack initiation and growth can be predicted using micromechanical analysis, and that the results are significantly affected by mechanical heterogeneity of the weldment.     

Residual stresses and fracture mechanics analysis of a crack in welds of high strength steels

This study presented the characteristics of residual stresses in welds of high strength steels (POSTEN60, POSTEN80) whose tensile strengths were 600 MPa and 800 MPa, respectively. Three-dimensional thermal elastic-plastic analyses were conducted to investigate the characteristics of welding residual stresses in welds of high strength steels through the thermal and mechanical properties at high temperatures obtained from the elevated temperature tensile tests. A finite element analysis method which can calculate the J-integral for a crack in a residual stress field was developed to evaluate the J-integral for a centre crack when mechanical stresses were applied in conjunction with residual stresses.The results show that the volumetric changes associated with the austenite to martensite phase transformation during rapid cooling after welding of high strength steels significantly influence on the development of residual stresses in the weld fusion zone and heat-affected zone. For a centre crack in welds of high strength steels where only residual stresses are present, increased tensile strength of the steel, increased the J-integral values. The values of the J-integral for the case when mechanical stresses are applied in conjunction with residual stresses are larger than those for the case when only residual stresses are present.     

Effects of crack size and weld metal mismatch on the has cleavage toughness of wide plates

The heat affect zone (HAZ) is in many cases considered to be the most critical part of a weldment. In this paper, the effect of crack size and weld metal mismatch on the HAZ cleavage toughness of wide plate specimens with X-groove has been investigated by the J-Q-M theories and a simple micromechanism for cleavage fracture. Two crack sizes have been studied (a/w = 0.1 and 0.3). In the analyses, the HAZ yield strength is assumed to be higher than the base metal. For each crack size, weld metal local overmatch and local evenmatch with respect to the HAZ are considered. For a given global strain, the results indicate that weld metal overmatch and evenmatch yield the same crack tip loading in terms of J-integral for a/w = 0.3. For a/w = 0.1, overmatch gives lower crack tip loading than evenmatch. For a given crack tip loading, weld metal local evenmatch in general results in less effective crack tip loading than the overmatch. Overmatch is detrimental to HAZ toughness, but this detrimental effect becomes less significant when the crack size decreases.     

On the evaluation of the J-integral by a plastic crack tip element

Two crack tip elements are formulated for a stationary, mode I plastic crack in planar structures using hybrid assumed stress approach, based on the secant modulus and the Newton-Raphson schemes, respectively. The stress distribution in the crack tip element is assumed to be the HRR field superimposed by the regular polynomial terms. The formulated (hybrid) crack tip elements are compatible with the isoparametric element so that they can be used conveniently along with the conventional displacement-based finite elements. The intensity of the HRR stress field, the J-integral, is determined directly from the finite element equations together with the nodal displacements. The dominance of the HRR stress field at the crack tip is pertinent to the present approach, which depends on geometry and loading conditions. Since the J-integral is globally path-independent for nonlinear elastic materials (deformation plasticity model), in order to assess the accuracy and efficiency of the methodology as compared to the contour integration approach, numerical studies of common plane-stress cracked configurations are performed for these materials. The results indicate that for a sufficiently small crack tip element size, J from the present approach correlates well, within 6 percent difference, with that from the contour integration for a wide range of material hardening coefficients if the HRR zone exists at the crack tip. These highly accurate results for J from the crack tip stresses could not be achieved without using (newly) modified variational principles and a refined numerical technique. It should be emphasized that the present methodology also can be applied to cracks in J ₂ flow materials under HRR dominance. In such case, the J integral may not be globally path independent, and hence it now must be determined from the stress and strain fields near the crack tip.     

The value of the J-integral at the onset of crack extension from a weld defect: Weld material is softer than parent material

The paper addresses the problem of crack extension in a weld in an engineering structure for the case where the weld crack is parallel to the plane of the weld, a situation for which the J-integral is path independent with regard to any contour surrounding a crack tip. Assuming that crack extension is associated with the attainment of a critical crack tip opening displacement _w, a theoretical analysis based on the strip yield representation of plastic deformation shows, for the case where the weld material is softer than the parent material, how the relation between the value of J at the onset of crack extension and _w depends on the flow properties of the weld and parent materials, the crack size and the weld thickness.     

Crack deflection by the transformable particles dispersed in composites

The crack deflection in transformable particle-reinforced composites is studied in the present paper.The contribution of phase transformation on the crack tip J_k-integral (k = 1, 2) is explicitly determined bythe material configurational theory. For the crack deflection angle from its original crack path induced by thephase transformation it can be shown that the crack initiates in the direction along which the potential energyrelease rate in terms of the crack tip J_k-integral possesses a stationary (maximum) value. The influence of oneindividual particle near the crack tip on the crack deflection is studied by accounting for both dilatant and sheartransformation components. Furthermore, an FEM method is developed to model the stress-induced phasetransformation on the basis of a macroscopic phenomenological constitutive model where multiple particlesare taken to be non-uniformly distributed in a matrix.Numerical simulations are performed to observe the crackdeflection by a cluster of particles. The results show a significant non-symmetric stress distribution locally atthe crack tip, causing the crack to deflect. It is found that regions in the material with a higher volume fractionof transformable particles tend to deflect the crack growth more.     

Quasi-static and dynamic fracture behavior of composite sandwich beams with a viscoelastic interface crack

Fracture analysis of sandwich beams with a viscoelastic interface crack under quasi-static and dynamic loading has been studied. Firstly, a three-parameter standard solid material model was employed to describe the viscoelasticity of the adhesive layer. And a novel interfacial fracture analysis model called three material media model was established, in which an interface crack was inserted in the viscoelastic layer. Secondly, a finite element procedure based on Rice J-integral and Kishimoto J-integral theories was used to analyze quasi-static and dynamic interface fracture behavior of the sandwich beam, respectively. Finally, the influence of viscoelastic adhesive layer on the quasi-static J-integral was discussed. In addition, comparison of quasi-static Rice J-integral with Kishimoto J-integral under various loading rates was carried out. The numerical results show that the oscillating characteristic of dynamic J-integral is more evident with shorter loading rise time.     

A three-point bend specimen with partly tapered cross-section sides

The stress intensity factor and the J-integral have been derived analytically and numerically for a modified three-point bend specimen with partly tapered sides, for various crack lengths, taper and specimen cross-section proportions, in order to allow full-thickness testing of tapered samples, common in older steel structures, to obtain a fair effective fracture toughness value for a through thickness crack in inhomogeneous materials. The stress intensity factor is obtained with the approximate analytical method of Kienzler and Herrmann, based on the concept of material forces. The J-integral is calculated numerically with a 3D finite element model for a linear elastic material and an elastic ideal-plastic material. A simple single specimen fracture toughness evaluation procedure is proposed. It is found that the effect of taper in the range encountered in practice is small, of the order of a few percent.     

A new constraint based fracture criterion for surface cracks

A new methodology for predicting the location of maximum crack extension along a surface crack front in ductile materials is presented. Three-dimensional elastic-plastic finite element analyses were used to determine the variations of a constraint parameter (α_h) based on the average opening stress in the crack tip plastic zone and the J-integral distributions along the crack front for many surface crack configurations. Monotonic tension and bending loads are considered. The crack front constraint parameter is combined with the J-integral to characterize fracture, the critical fracture location being the location for which the product Jα_h is a maximum. The criterion is verified with test results from surface cracked specimens.     

Dielectric Breakdown Model For An Electrically Impermeable Crack In A Piezoelectric Material

The present work presents a strip Dielectric Breakdown (DB) model for an electrically impermeable crack in a piezoelectric material. In the DB model, the dielectric breakdown region is assumed to be a strip along the crack's front line. Along the DB strip, the electric field strength is equal to the dielectric breakdown strength. The DB model is exactly in analogy with the mechanical Dugdale model. Two energy release rates emerge from the analysis. An applied energy release rate appears when evaluating J-integral along a contour surrounding both the dielectric breakdown strip and the crack tip, whereas a local energy release rate appears when evaluating J-integral along an infinitesimal contour surrounding only the crack tip. Under small yielding conditions, the local energy release rate, if used as a failure criterion, gives a linear relationship between the applied stress intensity factor and the applied electric intensity factor.     

Effect of thermomechanical loads on the propagation of crack near the interface brittle/ductile

The purpose of this paper is to understand the combined effect of thermal and mechanical loading on the initiation and behaviour of sub-interface crack in the ceramic. In this study a 2D finite element model has been used to simulated mixed mode crack propagation near the bimaterial interface. The assembly ceramometalic is subjected simultaneously to thermomechanical stress field. The extent of a plastic zone deformation in the vicinity of the crack-tip has a significant influence on the rate of its propagation. The crack growth at the joint specimen under four-point bending (4PB) loading and the influence of residual stresses was also evaluated by the maximum tensile stress criterion. The J-integral at the crack tip is generally expressed by the thermomechanical local stresses. The results obtained show the effect of the temperature gradient ΔT, the size of the crack and the applied stresses on the J-integral.